Introducing
Your new presentation assistant.
Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.
Trending searches
AP Calculus AB: Riemann Sums and Trapezoidal Rule
19
By: Bryce Henney, Danny Freed and Chad Cutler
Definite Integral: the area bounded by the curve and the x-axis of f(x) from points a to b
In mathematics, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is an approximate technique for calculating the definite integral.
History
The trapezoidal rule is part of a group of formulas called the Newton–Cotes formulas. This is named after Isaac Newton and Roger Cotes.
Trapeziodal Rule
In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It may also be used to define the integration operation. The method was named after German mathematician Bernhard Riemann.
Riemann Sums
Comparing Estimations
5 subintervals
or
20 subintervals
For calculating Riemann Sums and Trapeziodal Rule the more subintervals used in the equation the more subintervals used means the more accurate the answer is.
Formulas
Subintervals
100 subintervals
Answer
Mr. Klein was playing his favorite monkey video game which records how many bananas cakes you can make in an hour. The graph located below shows the rate which he made the cakes. Find out how many cakes he made over the 6 hour time period by using three midpoint Riemann Sums.
Example 2
AP Calculus AB: Reimann Sums
And Trapeziodal Rule
Midpoint Riemann Sum
VS.
Right Riemann Sum
Left Reimann Sum
Left Riemann Sum
Answer
Example One
Find the area between [1,8] with 4 subintervals
Example One
Trapezoid Rule Formulas
Area ≈
or
Answer
What is the definite integral from [0,9] of y using left Riemann sums?
(using 3 subintervals)
Mr. Dureka was riding his moped around town during a nice sunday afternoon. The table above shows his velocity over a 10 hour span. Find his approximate distance in miles using trapezoidal rule from [1,10] with 4 subintervals.
Velocity (mile/hour)
Time (hours)
Velocity (mile/hour)
Example 2
Time (hours)
Answer